On the Stellar Disk Vertical Scale Height of Edge-on Galaxies from S⁴G

We select our sample from the S⁴G survey (Sheth et al., 2010). S⁴G set out to image a volume (D $<$ 40 Mpc), magnitude (B_corr $>$ 15.5 mag) and size (D₂₅ $>$ 1 arcmin) limited sample of more than 2300 nearby galaxies with the near-infrared camera (IRAC; Fazio et al. 2004) in the Spitzer Space telescope at 3.6 and 4.5 $\mu$m near-infrared bands. We use 3.6 $\mu m$ band and retrieved these from the Spitzer archives from the NASA/IPAC Infrared Science Archive website¹¹1https://irsa.ipac.caltech.edu. The choose of this apparent sample was motivated by the interest in having insights to the stellar distribution, free from dust obscuration and the availability of sufficiently high resolution ($\sim 1.07$ arcsec) imaging to characterize the disk scale height.

The galaxies must be edge-on or highly inclined with an inclination larger than $80^{\circ}$. We note that inclination values vary within the literature. The publicly available S4G catalog available via IRSA includes Hyperleda values for inclination — in the case of NGC 4244, the Hyperleda value for inclination is 65.4 deg, while Comerón et al. (2011a) measures an inclination of 82 deg. To avoid these inconsistencies, we estimate the disk inclination i of each galaxy using Hubble’s formula:

where $(b/a)$ is the disk axis ratio measured at $R_{25}$ and $q_{0}$ is the intrinsic flatness. We adopted $q_{0}$ measured by Yuan & Zhu (2004) using 14988 disk galaxies taken from the Lyon-Meudon Extragalactic Database. They reported a $q_{0}$ $\sim$ 0.11 $\pm$ 0.03 which is consistent with previous studies. The disk axis ratios were measured using the ellipse fitting technique implemented in Photutils, an Astropy package for source detection and photometry for astronomical sources (Bradley et al., 2020). To minimize bulge contamination, we constrain the ellipticity of the sample to $\epsilon$ $>0.78$. In order to completely rule out irregular and early-type galaxies, we constrain the morphological type T (also known as the numerical Hubble stage T) to $1\leq\text{T}\leq 8$ thus confining our data set to spiral galaxies from Sa to Sdm type. We only include nearby galaxies with a mean distance $D_{mean}$ less than 30 Mpc. The distances were collected from the NASA/IPAC Extragalactic Database²²2http://ned.ipac.caltech.edu (NED) database. Distances measured using cepheid variables and the tip of the red-giant branch (TRGB) stars are preferably used since they are among the most accurate for nearby galaxies (Lee et al. 1993). We choose the distances with the smallest uncertainties for galaxies that do not have cepheid and TRGB-based distances. We note that 87% of our sample have been measured using the Tully-Fisher method.

Considering the constraints mentioned above, the query results in a total of 65 galaxies having an ellipticity of $0.78\leq\epsilon\leq 0.91$, a mean distance of $\ 4.1\ \text{Mpc}\leq D_{mean}\leq 29.92\ \text{Mpc}$ and a morphological type $3\leq\text{T}\leq 8$ (Sb to Sdm). After inspecting the data set, 19 galaxies are dropped from the sample either because of a bright foreground star in front of the disk, a bad or noisy image or because the disk is relatively faint and hard to deblend from neighboring sources. Our final sample consists of 46 edge-on galaxies as listed in Table 1. The final sample has an ellipticity range of $0.78\leq\epsilon\leq 0.91$, a mean distance range of $4.1\ \text{Mpc}\leq D_{mean}\leq 29.23\ \text{Mpc}$ and a morphological type range of $3\leq\text{T}\leq 8$ (Sb to Sdm) essentially dominated by later types of late-type galaxies with $5\leq\text{T}\leq 8$ (Sc to Sdm).

Although data from S⁴G catalog have already been through basic calibration and processing, further cleaning and background subtraction are necessary before the images can be used for further analysis. We use Photutils https://photutils.readthedocs.io/en/stable/ packages for the image processing. We adopt the following steps to clean the images properly. First, we estimate the sky background and subtract by applying the Background2D technique using the Source Extractor algorithm implemented in Photutils. This algorithm uses the sigma-clipping³³3The sigma-clipping method is a technique in which data outliers of a sample are rejected. If the sample is to be considered to have a Gaussian distribution, deciding on which data points are to be rejected or kept depends mainly on the value of each data point’s standard deviation from the sample mean $\sigma_{clip}$. method for which we adopted the default value of $\sigma_{clip}=3$. Generally, the estimated sky background agrees with the sky value given by the S⁴G catalog. The second step is to isolate the galaxy from other foreground and background sources using image segmentation techniques. This process can be done in Photutils using the detect_source() function. To detect sources properly, a threshold⁴⁴4The threshold value is a limit pixel value from which pixels are considered whether as a source or a part of the background. value is required. This is obtained using the detect_threshold() function. However, source segmentation cannot set apart overlapping sources. Fortunately, the deblend_sources() in Photutils can deblend sources – i.e. detect and separate overlapping sources into individual ones – using a multi-threshold technique. When the data has been segmented and deblended successfully, segments not related to the galaxy (i.e background and foreground stars) are removed. The third step is to use the masks produced by the segmentation image task in Photutils combined with the publicly–available S⁴G masks to properly isolate the galaxy and to minimize the contamination from remaining foreground stars and globular clusters. Finally, we rotated the images so that the galaxy mid-plane should be parallel to the $x$-axis of the image using position angle (PA) data from S⁴G. To illustrate this, Figure 1 shows a comparison between an uncleaned image and a background-subtracted, rotated and cleaned of UGC 09977.

The most convenient way to measure the scale height h_z is to fit a model to the vertical profile and retrieve the best-fit parameter values of the model. It is common to use the luminosity density profile L(z) instead of the surface brightness vertical profile. The light distributions along z of lenticular and spiral galaxies have been suggested to follow an exponential form (de Grijs & van der Kruit, 1996).

where $\mu$ is the central density and $h_{z}$ is the scale height. Disk galaxies having such a feature are often referred to as exponential disks. Other studies have proposed an isothermal disk model for light distribution profile (e.g van der Kruit and Searle 1981):

where $L_{0}$ is the luminosity density at galactic mid-plane and $z_{0}$ is a vertical scale parameter such as $z_{0}=2h_{z}$. In this case, the constant scale parameter $z_{0}$ at all $z$’s is given as (van der Kruit & Searle, 1981):

where $G=6.67\times 10^{-11}\ \text{N m}^{2}\ \text{kg}^{-2}$ is the gravitational constant and $\varrho_{0}$ the space density at the mid-plane. van der Kruit (1988) also proposed the following model to fit the vertical profile:

These functions have similar behavior at large-scale heights. However, the non-isothermal profiles are suitable for galaxies with thick and thin disk components which have non-continuous potentials at mid-plane (B10 and references therein).

Additionally, van der Kruit & Searle (1981) also proposed a two-dimensional approach to measure the scale height. Their model allows to fit the surface brightness along the radius and the vertical axis simultaneously giving the best-fit parameters values of the scale length and the scale height. It is the same model as the EdgeOnDisk model of the data analysis software Galfit (Peng et al., 2010). Assuming an isothermal disk, the proposed model is:

with $\mu_{\text{Jy}}(0,0)$ the central surface brightness and $K_{1}$ the modified Bessel function. A later study by YD6 proposed a generalized version of Equation 6. The latter allows additional flexibility by adding a new parameter, $n$, that permits a variation in the profile shape (i.e. the function that the profile follows). Here the surface brightness has units of flux density (usually in Jansky⁵⁵51 Jy = 10^-26 W m^-2 or Jy):

where f(z) = $\operatorname{sech}^{2/n}(nz/z_{0})$ and $K_{1}$ the modified Bessel function. When $n\rightarrow 1$, Equation 7 becomes Equation 6 which is an isothermal disk having a sech² shape. Obviously, $n\rightarrow 2$ has the vertical component of (7) that follow the sech function model. In contrast, with $n\rightarrow\infty$, the last block of relation 7 becomes $f(z)\propto\exp(-z/h_{z})$. We now have an exponential disk of scale height $h_{z}$.

Both Equations 6 and 7 are exclusive to perfectly edge-on galaxies (i.e. $i=90^{\circ}$) since they do not consider the effect of inclination of highly inclined galaxies (i.e. $80^{\circ}\leq i<90^{\circ}$). To tackle this issue, 3D models have been proposed (e.g. Erwin 2015). These 3D models are essentially based on 2D models that, instead of computing pixels of a 2D image, they are computed on a native galactic disk three-axis coordinate system ($xd$, $yd$, $zd$), where these axes are orthogonal to the galaxy’s semi-major axis of the disk, respectively (Erwin, 2015); Figure 7 from Erwin (2015) illustrates this approach for an inclined spiral galaxy, the transformation from a two-axis image coordinate system ($x,\ y$) to the galactic disk there-axis coordinates uses the inclination $i$ and takes the line of sight $s$ into account. It is common to use cylindrical coordinates instead of galactic disk coordinates with $R=(x_{d}^{2}+y_{d}^{2})^{1/2}$ is and $z=z_{d}$. The generalized model in terms of luminosity density is:

We measure the scale height by fitting the vertical profile to a known model. The pixel values of images in units of flux density (MJy per steradian⁶⁶61 MJy = $10^{6}$ Jy; 1 steradian = $4.25\times 10^{10}\ \text{arcsec}^{2}$ for the S⁴G images) have to be converted into units of surface brightness (mag arcsec^-2). For the 3.6 $\mu$m band of the S⁴G survey, the zero point flux density in Jansky is 280.9 Jy (Oh et al., 2008). Basically, the conversion from MJy/sr to mag arcsec^-2 for the 3.6 $\mu$m is given by the relation:

with $S_{3.6\ \mu\text{m}}$ the pixel value in MJy/sr.

To smooth and remove outliers in our data, we first generate a 2D Gaussian function of FWHM = 2.2 arcsec using the Astropy.convolution attribute Gaussian2DKernel (Astropy Collaboration et al., 2013, 2018) and convolve the latter with the background-subtracted, cleaned and rotated images. In the following, we introduce the fitting procedure for the 1D, 2D and 3D methods:

We first use the 1D method for two-component disk investigation as the existence of such a feature can be easily noticeable by observing the profile. We then average the values of pixels along the image’s x-axis. This allows having an averaged vertical profile that is converted into surface brightness units using Equation 9. Next, we convolve the model with a 1D Gaussian kernel with an FWHM of 2.1 arcsec since the images were previously smoothed. Here we use the sech² and exponential functions as models considering the vertical profile shape at extreme cases ($n\rightarrow 1,\ N\rightarrow\infty$ respectively, see Equation 7). We fit our image to a two-component model of each of the two mentioned above using lmfit (Newville et al., 2016). This Python package includes a large number of methods for curve fitting. We choose the Least-Squares algorithm returning a reduced chi-squared value $\chi^{2}_{\nu}$ when the fit is done. This parameter gives an insight into the quality of fits. Theoretically, a good fit has $\chi^{2}_{\nu}=1$. However, a non-biased value of this parameter requires the data to be weighted properly. We use the variance map of the images as weights for our data. We consider that a galaxy shows the presence of a thick disk when the two-component fit is esteemed to be successful i.e. the resulting scale height relative uncertainty of each component is lower than 30% and $\chi^{2}_{\nu}\sim 1$. In the case $\delta h_{z\ thin}/h_{z\ thin}<30\%$, $\delta h_{z\ thick}/h_{z\ thick}\geq 30\%$ and $\chi^{2}_{\nu}\sim 1$, we treat the galactic disk as a single-component disk. Else, we consider the fit unsuccessful.

We also employ the 1D method box model approach as a way to track the variation of the scale height along the radius giving us the radial profile of the scale height. We retrieve the vertical profiles along the radius using a similar approach as the “BoxModel” task within the NOD3 program (Müller et al., 2017). We divide the galaxy into small boxes instead of averaging along the entire length of the galaxy. Pixel values within each box are then averaged along the y-axis. This enables us to obtain the vertical profiles along the radial extent of the galaxy that can be fitted to a model. We fit the profile using a single component sech or exponential functions. We do not use the sech² model here since previous papers have shown that vertical profiles are steeper than the sech² model when observed from specific radii (Banerjee & Jog, 2007). We handle the 2D approach using the most commonly used and extensively tested data analysis software Galfit (Peng et al., 2010) instead of python packages. This program is widely used for galaxy fitting using the 2D method. As mentioned previously, the Galfit model for edge-on galaxies (the EdgeOnDisk model) takes on the form of Equation 6. Galfit uses a Least-Squares algorithm that uses Levenberg–Marquardt technique to perform the fits yielding a value of $\chi^{2}_{\nu}$:

where $\nu$ is the number of degrees of freedom, $Nx$ and $Ny$ the image dimensions, $f_{\text{data}}(x,y)$ the flux of the $(x,y)$-pixel, $f_{\text{model}}(x,y)$ the sum of $M$ functions of $f_{i}(x,y;\ \alpha_{1},\ ...,\alpha_{n})$, with $N$ free parameters $(\alpha_{1},\ ...,\alpha_{n})$ in the above model and $\sigma(x,y)$ the Poisson error that requires the image gain and readout noise⁷⁷7The gain and readout noise are quantities that characterizes the image sensors used in a telescope. Gain is the amount of amplification as the detected charges are converted into voltages. Readout noise is the noise of the amplifier. information as weights. These can be found in the image header file. Input images need to be in units of count. Therefore, we convert pixel values of the image from MJy/sr to counts by multiplying each pixel value with the exposure time and dividing it by the flux conversion factor. We choose to fit images using a single component edge-on-disk model for simplicity and to minimize computing time. We keep the background value fixed while the PA and galaxy center parameters are left to vary during the fitting process.

Because Galfit is essentially software for 2D fitting, we perform 3D method fits using Imfit, a program for astronomical image fitting (Erwin, 2015). In this regard, we use the ExponentialDisk3D function derived from Equation 7 as a model. The latter utilizes the same principle as explained in Section 2.3 to fit the 2D image onto the 3D model. Among the different minimization algorithms and statistics that Imfit has, we adopt the Levenberg–Marquardt technique coupled with the Poisson maximum-likelihood ratio statistic as recommended by (Erwin, 2015) to make sure fits are accurate and performed as fast as possible.

In Table 2 we summarize the measured scale height derived from 1D, 2D and 3D methods. The average uncertainties are the total errors i.e. the combination of statistical and systematic errors. We find that 2D and 3D methods produce the smallest uncertainties and are typically in good agreement with each other. The number of galaxies $N$ for which the fits were successful are given in column 2 in Table 2. We choose the model with a high success rate and small uncertainties for the statistical analysis part of this paper. This leads us to consider only the results from the 2D method for the one-component disk analysis. The 1D sech² and the sech box model results are used for the two-component disks analysis and the radial profile of the scale height, respectively.

The histogram of the uncertainties for the 2D model is shown in the top panel of Figure 3. It gives the percentage of the uncertainties distribution relative to the measured scale height. The uncertainties distribution resembles a left-skewed normal distribution at first glance with the exception of a gap in the middle. However, its Pearson skewness coefficient is estimated to be -1.96 which falls into the acceptable range in order to prove normal distribution. The presence of the gap most likely originates from the strong influence of galaxy distance errors on $h_{z}$ uncertainties (see Section 2.5.2). In fact, the distance measured using the TRGB technique yields less uncertainty than the Tully-Fisher distance. Therefore, the two different distance measurement may have introduced the gap in the left panel of Figure 3. However, due to the presence of a random error as discussed in Section 2.5.2 the gap is not observed in the histograms of errors for 1D models and they instead show a bimodal trend. The histogram of uncertainties for 1D sech² model is shown in the bottom panel of Figure 3.

Figure 4 compares the scale heights results from the 1D models to $h_{z}$ to the 2D models. The average h_z from the box sech model and the 2D sech² is plotted on the left panel. Right panel shows the thick disk scale height from the 2 disk sech² model as a function for the 2D scale height. The left panel of Figure 4 suggests that when flaring is considered the 1D sech model has systematically slightly higher $h_{z}$ than the 2D sech² model. It also implies that the 2D sech² model may slightly miss the flaring outer part of the disk, if we assume the systematic difference in $h_{z}$ between the sech² and sech models can be ignored since both models converge to the exponential model at large radius. However, the two measurements are consistent with their uncertainties. The right panel of this figure shows that the 2D sech² single-component measurements are consistent with the measurements of the thick component of the 1D sech² two-component model. The results of the right panel suggest that the 2D sech² model tends to measure the relatively thicker disk component even if a thin disk exists.

We present the best-fit parameters for the single component disk in Table 3. While uncertainties on h_z and h_R are total errors, uncertainties on the central surface brightness are statistical errors only. Both scale heights and central surface brightness are corrected for inclination using the model given by Equations 11 and 12 respectively.

Figure 5 shows a comparison between scale heights from the 2D and 3D methods. This shows that the two methods are in good agreement, displaying a smaller scatter around the identity line, compared to the plots in Figure 4 for the 1D and 2D methods . This indicates that the GALFIT and IMFIT models are consistent despite the added flexibility in profile shape that Imfit allows with the insertion of the parameter $n$.

We use the 1D sech² model to investigate two-component disks. Best-fit parameters are shown in Table 4. We find that close to two-thirds of our galaxies show the presence of a thick disk considering our sample is composed of nearby late-type spiral galaxies. In comparison, Comerón et al. (2018) found that thick disks are always present using a sample of mainly distant and early-type galaxies. It has been established for the Milky Way that the thin disk has two distinct components: a “young thin disk” dominated by young OB associations and an “old” thin disk with older redder stars (YD6). The young thin disk, the old thin disk and the thick disk of the Milky Way usually have scale heights of $\sim 0.1\ \text{kpc},\ \sim 0.3\ \text{kpc}$, and $\sim 1\ \text{kpc}$, respectively (Reid & Majewski, 1993; Larsen & Humphreys, 2003). However, all of the thick disks in our sample have $h_{z\ \text{thick}}<1$ kpc and a few galaxies have $h_{z\ \text{thin}}\sim 0.1$ kpc suggesting that the two-component disk we find could correspond to the young and old thin disks. Furthermore, our near-infrared insight at 3.6 $\mu$m provides us with a is dust-free view and is likely to contain most of the old stellar population. This implies that the two components we found are indeed the old thin disk and the thick old stellar disk. Our average scale heights of $\bar{h}_{z\ \text{thin}}=0.14\pm 0.07$ kpc and $\bar{h}_{z\ \text{thick}}=0.33\pm 0.16$ kpc are smaller than the dust-free measurements reported by YD6 ($\bar{h}_{z\ \text{thin}}\sim 0.27$ kpc; $\bar{h}_{z\ \text{thick}}\sim 0.59$ kpc) using sech² models on B-, R- and K-band data. However, the fact that our inclination-uncorrected scale heights ($\bar{h}_{z\ \text{thin}}=0.22\pm 0.07$ kpc; $\bar{h}_{z\ \text{thick}}=0.52\pm 0.18$ kpc) matched those from YD6 which does not explicitly mention an inclination correction implies that the inconsistency might be due to projection effect. We also compare our scale heights with those from Comerón et al. (2011a, b), who examined the vertical structure of nearby galaxies using S⁴G images, with a few galaxies overlapping with our sample. For example, our two-component fits for NGC 4244 were unsuccessful, whereas Comerón et al. (2011a) identified a faint thick disk on the galaxy’s near side using a single-component exponential model across varying heights $z$. While we find a single-component $h_{z}=0.21$ kpc (uncorrected for inclination of $h_{z}=0.35$ kpc), they measured an average $h_{z\ \text{thin}}\sim 0.35$ kpc for this galaxy. For the other overlapping galaxies, such as NGC 3501 the measured scale height of ($h_{z\ \text{thin}}=0.15$ kpc; $h_{z\ \text{thick}}=0.36$ kpc inclination corrected) and (uncorrected for inclination, $h_{z\ \text{thin}}=0.22$ kpc; $h_{z\ \text{thick}}=0.51$ kpc) are in agreement with results from Comerón et al. (2011b) (average $h_{z\ \text{thin}}\sim 0.20$ kpc; $h_{z\ \text{thick}}\sim 0.59$ kpc). On the other hand, the scale height of NGC 4330 is lower compared to the literature (e.g Comerón et al. 2011a). We measured a scale height of $h_{z\ \text{thin}}=0.11$ kpc; $h_{z\ \text{thick}}=0.31$ kpc (uncorrected for inclination of $h_{z\ \text{thin}}=0.16$ kpc; $h_{z\ \text{thick}}=0.45$ kpc) for this galaxy compared to their measurements (average $h_{z\ \text{thin}}\sim 0.18$ kpc; $h_{z\ \text{thick}}\sim 0.74$ kpc) from Comerón et al. (2011b). This discrepancy is likely due to the difference in inclination correction and model fitting as Comerón et al. (2011b) apply separate corrections for each disk component and utilize a hydrostatic equilibrium solution model instead of the simpler sech² function.

Ratios of thick and thin disk scale heights $h_{z\ \text{thick}}/h_{z\ \text{thin}}$ are also presented in Table 4. We find an average $h_{z\ \text{thick}}/h_{z\ \text{thin}}=2.65\pm 0.56$. In comparison, YD6 find an average $h_{z\ \text{thick}}/h_{z\ \text{thin}}=2.5$. It is important to reiterate that we choose to use the near-infrared data in this paper in order to better trace the older stellar populations that dominate these stellar structures. The distribution of scale height ratios is shown in Figure 8. Because the ratio of thick-to-thin disk stellar mass has been shown to be related to the global kinematics of galaxies (Vieira et al. 2022), it is also interesting to probe for a correlation between $h_{z\ \text{thick}}/h_{z\ \text{thin}}$ and $V_{\text{flat}}$ or the maximum velocity $V_{\max}$. Figure 9 illustrates that galaxies with a thick disk component have higher $V_{\text{max}}$ values (on average $104\pm 32.4\text{km s}^{-1}$) than those without this disk feature (on average $74.2\pm 13.6\text{km s}^{-1}$). This observation confirms the correlation between dynamical mass and disk accretion. This aligns with the evidence suggesting the formation of massive galaxies through mergers, as noted in Qu et al. (2011), which implies the presence of a thick disk.

Figure 10 shows the successful vertical disk profile fits using two sech² models. It can be observed that both disks are generally approximately symmetrical relative to the galactic mid-plane as most galaxies of our sample. The averaged profile is represented by the squared data points, the red solid line is the total best-fit model, the dashed blue line corresponds to the thin disk model and the dotted and dashed green line is the thick disk model.

The radial profiles of the vertical disk scale heights are shown in Figure 12 to 14 and the profiles of all the galaxies in our sample are presented in Figure 15. These figures show that almost all the galaxies in our sample have an increasing disk thickness from the center to the outer part of the galaxies. The flaring amplitude given as ($h_{z,R_{25}}-h_{z,R=0})/h_{z,R=0}$ varies for each galaxy but only two galaxies (IC5052 and NGC5023) have less than 10 % disk flaring amplitude. Therefore, outer disk flaring is observed for all the galaxies in our sample. However, using observation of edge-on galaxies in B, V, R and I band imaging, de Grijs & van der Kruit 1996 noted that the observed disk flaring could be attributed to optical edge effect and warps. Furthermore, de Grijs & van der Kruit (1996) found through visual inspection of the radial profile of the scale heights that the flaring is more important in terms of amplitude in early-type disks than in later-type ones. To check if our sample follows this tendency, we plot the ratio of the scale height at the apparent radius and the galaxy center $h_{z,R_{25}}/h_{z,R=0}$ against the morphological type T (Figure 16). Note that the apparent radius $R_{25}$ (indicated in Figure 12) has been measured in the B-band and retrieved from the Hypercat-Lyon-Meudon Extragalactic Database⁸⁸8http://leda.univ-lyon1.fr (HyperLEDA, Makarov et al., 2014). As proved by de Jong (1996), galaxies tend to be bluer with increasing radius which means that $R_{25}$ measured in the B-band might be bigger than the apparent radius as seen in the 3.6 $\mu\text{m}$ imaging. It can be seen from Figure 16 that the increase in scale height is indeed more evident in earlier type galaxies than in later type ones (with correlation coefficients $R_{Pearson}=-0.32$ and $R_{Spearman}=-0.29$, a p-value of 0.03 and given the fact that only 4 galaxies of our sample have $T<5$). The best-fit relation is:

with $h_{z}(R_{25})/h_{z}(R=0)$ the disk flaring amplitude and T the morphological type. This trend is thought to be caused by the change in bulge contribution to the total light of the galaxy de Grijs & van der Kruit (1996) as it evolves along the Hubble sequence. However, most of our galaxies do not have a prominent bulge and the bulge contamination usually affects the inner part of the disk therefore should not influence the flaring of the outer disk. In fact, observations from Lange et al. (2016) show that disks systematically exceed bulges in terms of size by a factor of $\sim 0.12$ to 0.69 dex for spiral galaxies considering all stellar masses between $\sim 10^{7}-10^{12}\ M_{\odot}$. Nonetheless, the effect of bulge contamination requires a more in-depth investigation with a more exhaustive sample.

We discuss in this section possible correlations that exist between the measured scale height with other galaxy properties.